# easy m1 questionWatch

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#1
I'm just wondering when a question says show that the particles collide do i just put them equal to eachother.

For example...... A coastguard station O monitors the movements of ships in a channel. At noon, the station's radar records two ships moving with constant speed. Ship A is at the point with the position vector (-3i + 10j) km relative to O and has velocity (2i + 2j)kmh^-1. Ship B is at the point with position vector (6i + j)km and has velocity (-i + 5j)kmh^-1.

a) show that if these ships maintain these velocities they will collide.

would i just do.....
(-3i + 10j) + (2i + 2j)t = (6i + j) + (-i + 5j)t

then where would i go???????????????
0
8 years ago
#2
|(-3i+10j)+(2i+2J)t|=|(6i+j)+(-i+5j)t|
or, (-3+2t)^2+(2t+10)^2=(6-t)^2+(5t+1)^2
or,............................. ..........i guess u can solve it now. just expand and find value of t.
0
8 years ago
#3
(Original post by the mathematician)
|(-3i+10j)+(2i+2J)t|=|(6i+j)+(-i+5j)t|
or, (-3+2t)^2+(2t+10)^2=(6-t)^2+(5t+1)^2
or,............................. ..........i guess u can solve it now. just expand and find value of t.

A solution to that merely shows that they can be at the same distance from the station; not that they will collide.

(Original post by Byrney11)
would i just do.....
(-3i + 10j) + (2i + 2j)t = (6i + j) + (-i + 5j)t

then where would i go???????????????
Yes.

Now equate coefficients for i and find the value of t for which they have the same i co-ordinate.
Show that this value of t puts them at the same j co-ordinate.

This shows that at the time they will have the same i and j co-ordinate, and hence collide.
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